Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> con...Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.展开更多
Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<...Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<sub>m</sub></sup> of cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup>-action with the fixed point set of（n-l<sub>i</sub>）-dimensional submanifolds of M<sup>n</sup>.展开更多
The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curv...The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distribution H of this bundle is integrable if and only if M has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and its first normal space is vertical.展开更多
The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.
Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in ...Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in R^(2n-α(n)-1), and prove that the Stiefel-Whitneynumber W_(n-α(n))W_α(n) (M^n)=0 iff M^n is cobordant to a smooth closed n-manifold N^n, whereN^n immerses itself in R^(2n-α(n)-1).展开更多
文摘Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.
文摘Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<sub>m</sub></sup> of cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup>-action with the fixed point set of（n-l<sub>i</sub>）-dimensional submanifolds of M<sup>n</sup>.
文摘The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distribution H of this bundle is integrable if and only if M has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and its first normal space is vertical.
文摘The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.
基金Project supported by the National Natural Science Foundation of China.
文摘Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in R^(2n-α(n)-1), and prove that the Stiefel-Whitneynumber W_(n-α(n))W_α(n) (M^n)=0 iff M^n is cobordant to a smooth closed n-manifold N^n, whereN^n immerses itself in R^(2n-α(n)-1).
